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miley23
 3 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, 13, and 5 + 4i
A. f(x) = x4  8x3  12x2 + 400x  1599
B. f(x) = x4  200x2 + 800x  1599
C. f(x) = x4  98x2 + 800x  1599
D. f(x) = x4  8x3 + 12x2  400x + 1599
miley23
 3 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, 13, and 5 + 4i A. f(x) = x4  8x3  12x2 + 400x  1599 B. f(x) = x4  200x2 + 800x  1599 C. f(x) = x4  98x2 + 800x  1599 D. f(x) = x4  8x3 + 12x2  400x + 1599

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whpalmer4
 3 years ago
Best ResponseYou've already chosen the best response.0We have roots of x = 3, 13, and 5+4i. We're going to need a conjugate to 5+4i also, because the complex roots come in pairs, so that will be 54i. Now the roots are simply the places where the factors of the polynomial = 0, so we can write our factored polynomial as \[f(x) = (x3)(x+13)(x54i)(x5+4i) = 0\] Now it's just some pencilpushing to multiply that expression out to get f(x) = x^4 + more terms. I would suggest multiplying the (x54i) and (x5+4i) terms first, as doing so will eliminate the terms containing i (remember that i^2 = 1).
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